# How To Use the Python Square Root Function

There are many situations in which you will want to find the square root of a function in a Python application.

Fortunately, Python includes some very powerful functionality for calculating square roots.

In this article, I will teach you how to use the Python square root function. I will also show you how to calculate square roots without this function, and how to calculate the square root of every element in an outside data structure.

## Table of Contents

You can skip to any particular section of this Python tutorial using the links below:

- What is a Square Root?
- The Python Square Root Function
- How To Calculate Square Root Without the Python Square Root Function
- Final Thoughts

## What is a Square Root?

It's hard to understand the square root without understanding squares first.

In mathematics, the square of a number is the value that is generated when you multiply a number by itself. Here are a few examples:

- The square of 2 is 4, since 2 times 2 is 4
- The square of 4 is 16, since 4 times 4 is 16
- The square of 8 is 64, since 8 times 8 is 64

In Python, these values are easy to calculate using the `**`

operator, which is used to calculate exponents.

The same examples that I used above are calculated using Python in the following code block.

```
2**2
#Returns 4
4**4
#Returns 16
8**8
#Returns 64
```

The square root function is almost like a backwards version of the square. It is the number that when multiplied against itself yields the square value.

A few examples (using the same mathematical relationships from before) are below:

- The square root of 4 is 2, since 2 times 2 is 4
- The square root of 16 is 4, since 4 times 4 is 16
- The square root of 64 is 8, since 8 times 8 is 64

These square roots were fairly easy to determine since they were small enough integers to be included in our elementary school times tables.

For larger numbers, it can be very difficult to calculate square roots. Fortunately, the Python square root function exists to make our life easy here. We'll learn about the Python square root function in the next section.

Return to the Table of Contents

## The Python Square Root Function

Python comes with a built-in `math`

module that contains many useful functions. One of these functions is `sqrt`

, which allows us to calculate square roots.

To use this function, you must first import the `math`

module into your application with the following command:

`import math`

Now that the `math`

module has been imported, we can call the `sqrt`

operator from the `math`

module using the dot operator. As an example, here's how you would use the `sqrt`

function to compute the square root of `4`

:

```
math.sqrt(4)
#Returns 2.0
```

The `sqrt`

operator works for numbers of any size, which is helpful. Here is an example of `sqrt`

applied to a very large number:

`math.sqrt(68564654987654321654984.3215)`

Here is the output

`261848534438.62222`

Depending on the purpose of your Python program, you may want to import exclusively the `sqrt`

function and not the entire `math`

module.

Here is how you modify your module import:

```
from math import sqrt
#instead of 'import math'
```

Since you did not import the entire `math`

module, you do not need to call the `sqrt`

function from the `math`

module using the dot operator. Instead, you can call the `sqrt`

function directly, like this:

`sqrt(100)`

Here is the output:

`10.0`

Return to the Table of Contents

## Calculating the Square Root of Every Element in a Python List

Let's say you had a Python list containing numbers, and you wanted to calculate the square root of every element in the list.

`my_list = [1, 4, 9, 16]`

Can you use the `sqrt`

function to do this?

Let's try it:

```
from math import sqrt
my_list = [1, 4, 9, 16]
sqrt(my_list)
```

Unfortunately, this will return `TypeError`

that looks like this:

`TypeError: must be real number, not list`

It is clear that the `sqrt`

function is not designed to work with lists. It is still possible to calculate the square root of every element in a list.

To do this, we will need to use a loop. Here's what this loops like:

```
from math import sqrt
my_list = [1, 4, 9, 16]
i=0
while i < len(my_list):
my_list[i] = sqrt(my_list[i])
i += 1
```

If you were to print out the `my_list`

list now, you would see that its values have each had the `sqrt`

function applied to them.

`[1.0, 2.0, 3.0, 4.0]`

Return to the Table of Contents

## How To Calculate Square Root Without the Python Square Root Function

It is possible to calculate Python square roots without using the `sqrt`

function.

This is because the square root function is the same as raising a number to the power of `0.5`

. We have already seen that the `**`

operator allows us to calculate exponents in Python. Here is how you could calculate the square root of `100`

without using the `sqrt`

function:

```
100**0.5
#Returns 10.0
```

To go back to our earlier example of computing the square root of the elements within a Python list, here is how you could refactor this code to avoid using the `sqrt`

function:

```
my_list = [1, 4, 9, 16]
i=0
while i < len(my_list):
my_list[i] = my_list[i]**0.5
i += 1
my_list
```

Return to the Table of Contents

## Final Thoughts

In this tutorial, you learned how to use `sqrt`

, the Python square root function.

I also explained the basics of square roots from a mathematical perspective and showed you how to calculate square roots in Python without the `math`

module.

I hope you enjoyed this tutorial. If you have any ideas or suggestions for future content, please email me!